Sprawdzić-(funkcje trygonometryczne)

[kyos]

Obliczyć pole trapezu




jak ktoś nie widzi to :

\(\displaystyle{ \sin 45 ^{0} = \frac{a}{3 \sqrt{2} } \Rightarrow a=3 \\ \\ \tg 45 ^{0} = \frac{3}{b} \Rightarrow b=3 \\ \\ P _{1} = \frac{1}{2} \cdot 3 \sqrt{2} \cdot \sin 45 ^{0} \Rightarrow P _{1} = 4,5 \\ \\ P _{2} = a \cdot b= 3 \cdot \sqrt{3} =3 \sqrt{3} \\ \\ P _{3} =? \\ \\ \sin 30 ^{0} = \frac{x}{6} \Rightarrow x=3 \\ \\ \cos 30 ^{0} = \frac{z}{3} \Rightarrow z= \frac{3}{2} \\ \\ P _{3} = \frac{1}{2} \cdot \frac{3}{2} \cdot 6 \cdot \sin 30 ^{0} =2.25 \\ \\ P=P _{1} + P _{2}+ P _{3}= 6.75 +3 \sqrt{3}}\)

[bb314]

\(\displaystyle{ P_1=\frac12\cdot3\cdot3\sqrt2\cdot\sin45^o}\)

\(\displaystyle{ \cos30^o=\frac{\sqrt3}{2}}\)

\(\displaystyle{ \frac{z}{3}=\ tg60^o=\sqrt3}\)